In his treatment of the Wittgensteinian paradox about rule-following, Saul Kripke represents the non-reductionist approach, according to which meaning something by an expression is a sui generis state that cannot be elucidated in more basic terms, as brushing philosophical questions under the rug. This representation of non-reductionism aligns with the conception of some of its proponents. Meaning is viewed by these philosophers as an explanatory primitive that provides the basic materials for philosophical inquiry, and whose nature cannot serve as an object for that inquiry. There is, however, an alternative way of conceiving of non-reductionism, which makes it possible to tackle philosophical questions about the nature of meaning head-on, and thus to respond to Kripke’s challenge in an illuminating manner.